Question

a piece of machinery depreciates $6000 the first year, $5700 the second year, and $5400 the third year. if the rate of depreciation is constant, what is the amount of depreciation of the piece of machinery in the sixth year? a $18,500 b $4500 c $36,500 d $4800

Explanation:

Step1: Identify the sequence type

The depreciation amounts are $6000, $5700, $5400,... This is an arithmetic sequence where the first term \(a_1 = 6000\) and the common difference \(d\) is \(5700 - 6000=- 300\) (or \(5400 - 5700=-300\)).

Step2: Use the arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\). We need to find the 6th term, so \(n = 6\), \(a_1=6000\), \(d=- 300\).

Substitute the values into the formula:
\(a_6=6000+(6 - 1)\times(-300)\)
\(a_6=6000+5\times(-300)\)
\(a_6=6000 - 1500\)
\(a_6 = 4500\)

Answer:

B. $4500